Method for installing cables in ducts using a pressurized fluid and a device for carrying out said method

ABSTRACT

Method and device for installing cables in ducts using a pressurized fluid, a fluid being applied which, under the operational pressure and operational temperature applied during the installation, is in a liquid state and which, under the ambient pressure and ambient temperature prevailing at the location of the installation, is in gaseous state. By applying such a fluid, the advantages of installing a cable using a liquid flow and using a gas flow may be combined, while the drawbacks respectively associated therewith are obviated.

[0001] The invention relates to a method for installing cables in ductsusing a fluid.

[0002] Such method, in which the fluid is a pressurized gas, isdisclosed, e.g., in EP-A-0,108,590. Said method has the advantage of thepropelling forces being evenly distributed over the length of the cable,so that installation is also possible in curved sections. In the eventof conventional pulling of a cable, all force is concentrated in theinitial part of the cable, as a result of which installation in curvedsections is a problem.

[0003] A method of the above type, in which the fluid is water, isdisclosed, e.g., in GB-B-2,122,367. Using fluid in general has theadvantage that the friction between the outside cable wall and the innerduct wall is less than in the event of using air, since the cablefloats, at least in part, in the fluid. A further advantage is that thecapacity of the pump used for introducing the fluid into the duct, inthe event of a liquid may be less than in the event of a gas, since aliquid has a higher viscosity than a gas. This is particularlyadvantageous for larger duct diameters. It may also be an advantage thatthe pressure drop in the event of using a liquid is linear, and there istherefore exercised a constant entraining force along the duct section.A still further advantage is that, in the event of using a liquid,electrostatic effects, as a result of which the cable is attracted tothe duct wall, in most cases are capable of being cancelled out.

[0004] Using liquids, such as water, however, also has its drawbacks. Inmost cases, after installing the cable the water must be removed fromthe duct. In the event of optical-fibre cableswithout a metal waterscreen, there may occur fibre breakage in the presence of water as aresult of stress corrosion. In the event of copper cables without waterscreen, the electrical properties will deteriorate. Finally, freezing ofthe water may cause damage. Another problem in the event of using wateris that, in elevated parts of the duct section, particularly in ductsections featuring relatively steep parts, in a water-filled duct theremay still remain enclosed an air bubble, as a result of which therearises additional friction in said elevated parts. Having such airbubbles escape is possible, though expensive, which is also true forusing a vacuum to the duct in advance.

[0005] An object of the invention is to provide for a method in whichthe drawbacks of installing using a liquid are lacking or are suppressedto a great extent, while the advantages are being maintained.

[0006] For this purpose, the invention provides for a method of theabove type, characterized in that a fluid is used which, under theoperational pressure and operational temperature used duringinstallation, is in a liquid state and which, at the ambient pressureand ambient temperature prevailing at the installation location, is ingaseous state.

[0007] The invention is based on the insight that, if use is made of afluid which at the operational circumstances prevailing at theinstallation of cables in ducts by, e.g., varying the pressure and/ortemperature, is brought to a liquid state and that at the ambientpressure and ambient temperature prevailing at the location ofinstallation is in a gaseous state, the advantages of installing using agaseous medium and installing with a liquid medium, may beadvantageously combined. After all, liquid is very suitable forinstalling, but hard to remove, while a gas has drawbacks in the eventof installation but is simple to remove. Generally, for this purpose usemay be made of a fluid which is in a liquid state at a preferablysignificantly lower pressure than the maximum permissible operationalpressure, or due to a temperature reduction, but which upon reducing thepressure or increasing the temperature, is in a gaseous state onceagain.

[0008] The method according to the invention is particularly suitable touse in situations in which the installation duct bridges a difference inaltitude, as in mountainous regions and in high-rise construction.

[0009] With the method according to the invention, it is possible to usea fluid, which is subject to such a pressure difference that itexercises an entraining force on the cable to be installed. It is alsopossible, however, to utilize the fluid exclusively to have the cablefloat and to further install it using a combination of pushing andpulling. In this case, the fluid either flows with a velocity lower thanthe propulsion speed of the cable, or the fluid may even flow in adirection opposite to the propulsion direction of the cable.

[0010] Examples of fluids for which the liquid state is attainedsubstantially using a pressure increase are, e.g., HFKs(hydrofluorocarbons), ammonia, propane, butane, fluids which nowadaysare used as cooling liquids and are, to a certain extent,environmentally safe. LPG (liquefied petroleum gas), too —a mixture ofpropane and butane—may be used as a fluid. Another example are the CFCs[=chlorofluorocarbons) which, however, are less desirable in view of thedamage incurred by the environment.

[0011] As an example of a fluid with which the liquid state is attainedsubstantially by using temperature reduction, CO₂ may be referred to.The advantage of CO₂ is that it is neither flammable nor aggressive. Inthe event of using CO₂, the pressure should preferably remain in excessof 5 bar (triple point) in order to prevent the formation of solidmatter, which would impede the installation. At a normal operationalpressure, the temperature should be significantly lower than the ambienttemperature, e.g., −60° C., in order to maintain the CO₂ in the liquidstate. At such a low temperature, the friction between cable and ductwall will decline. The density of CO₂ is 1.1 g/cm³, somewhat higher thanthat of water, and makes it possible to exercise a great floating effecton a cable.

[0012] Table 1 offers an overview of examples of applicable fluids andtheir physical properties.

[0013] A second option, which is based on the concept on which theinvention is founded, is, particularly in the event that the applicablefluid is recycled, to first have the duct in which the cable is to beinstalled blown through with the gaseous state of the fluid which later,at the installation proper of the cable, will be used in the liquidstate. During the subsequent further filling of the duct with a fluidwhich is now, as a result of higher pressure and/or lower temperature,in the liquid state, the gas in the duct will also condensate to form aliquid. Due to said condensation of the gas in the duct, the problemreferred to above of the inclusion of air bubbles is also obviated.

[0014] In addition, the invention comprises a device for carrying outthe method according to the invention, provided with means to couple afluid flow to the input end of the duct in order to fill the duct withthe fluid, and with means to introduce the cable into the input end ofthe duct, characterized in that there are provided means to pressurizethe fluid and/or reduce its temperature in order to bring the fluid tothe liquid state, the means comprising a stock vessel and/or acompressor and/or cooling means, which compressor and/or cooling meansare coupled to the input end of the duct.

[0015] Below, the invention will be explained in greater detail on thebasis of exemplary embodiments with reference to the drawing. In it,

[0016]FIG. 1 shows a first arrangement for carrying out the methodaccording to the invention;

[0017]FIG. 2 shows a second arrangement for carrying out the methodaccording to the invention;

[0018]FIG. 3 shows a third arrangement for carrying out the methodaccording to the invention;

[0019]FIG. 4 shows a fourth arrangement for carrying out the methodaccording to the invention; and

[0020]FIG. 5 shows a fifth arrangement for carrying out the methodaccording to the invention.

[0021] In the figures, equal parts are denoted by equal referencenumerals.

[0022]FIG. 1 shows a first arrangement. A cable 1 is wound on a reel 2and must be introduced into a duct 3 using an input device 4. Said inputdevice may be of the type disclosed in EP-A-0,292,037 and during theinstallation, if so desired, the propulsion force of the cable may besupplemented by forces exercised using pressure rollers 5, 5′accommodated in the input device 4. The fluid is pumped from a stockvessel 7 using a compressor or a compressor/cooler 6 as a liquid by wayof an inlet aperture 8 of the input device 4 into the duct 3. The end ofthe duct 3 may be open. If use is made of a flammable fluid, it isundesirable that it flow freely from the open end of the duct 3. It isquite possible, however, to burn off the fluid at that location.

[0023] Another option is to recycle the fluid. For this purpose, thefluid may be collected in a vessel at the end of the duct. In doing so,it is desirable to also place a compressor which pumps the fluid intothe vessel at the end of the duct. As a result, the fluid pressure atthe end of the duct may be low, which benefits the entraining forcesexercised in the duct.

[0024] For the benefit of recycling, the fluid, as FIG. 2 shows, mayalso be returned, by way of a return pipe 9, to the input end of theduct, a so-called forced circulation. As a return pipe, there may beused any other pipe already available under the ground, or above theground there may be provisionally laid a second pipe, e.g., a hose. Thefluid is returned, by way of a feedback piece 10 and the return pipe 9,to the compressor 6. In the arrangement shown, there is also shown adifference in height between the input end and the output end of theduct 3. This gives rise, if the fluid in the return flow is a liquid, tothe advantage that the weight of the return-fluid column “presses” onthe input side of the compressor 6, as a result of which it only mustsupply the circulation pressure and not the hydrostatic pressure. Thismay be of importance if, e.g., ducts are installed in a substantiallyvertical direction in high-rise construction.

[0025] If the return pipe has too high a flow resistance, a compressorat the end of duct 3 may also offer a solution. It is simpler to use areturn pipe having a sufficiently large diameter, as a result of whichthe pressure drop over said pipe remains limited. The return pipe maypossibly be a duct enveloping the installation ducts. If it isundesirable for the return flow to have too low a temperature, e.g.,when using carbon dioxide, there may be placed a heat exchanger at thetransition from the installation duct to the return pipe, in order toheat up the return flow.

[0026] During the circulation, the fluid in the return pipe may becirculated in the form of gas or liquid. If the return flow is gaseous,the diameter of the return pipe 9 must be considerably larger than theone of the duct 3, since the gas must flow much more rapidly than theliquid. Upon circulation of liquid only, the compressor 6 must circulateonly liquid and there occur no temperature effects due to the liquidexpanding.

[0027] Ducts having a smaller diameter are easily filled over theirentire length upon pumping-in a liquid. For ducts having a largerdiameter, in which liquid columns “break” easily, the following solutionmay be chosen. First, the duct 3 is allowed to fill using the compressor6, the compressor supplying a pressure of, e.g., 10 bar. This is amplysufficient for a height difference of 50 m, since, when using, e.g.,liquid butane, each 10 m of rise, demands approximately 0.6 bar ofpressure. Filling may be simplified by venting or burning off, therebeing opened air-relief cock 12 at the highest point and the feedbackduct 9 being closed using a cock 13 on the compressor 6. There may alsobe several air-relief cocks if there are several local highest points.Once the liquid in the feedback piece 10 overflows the rim, feedbackduct 9 will fill with liquid. Once the feedback piece 10 and thefeedback duct 9 are entirely filled with liquid, the air-relief cock 12may be closed. Reservoir 7 is then closed off and the entry to thefeedback duct 9 on compressor 6 is opened. The system now is in the“circulation mode”. The entire operational pressure of compressor 5 maynow be used to circulate liquid. In order to compensate for the pressuredrop over feedback duct 9, there may be placed, as mentioned earlier, asecond compressor at feedback piece 10. Said circulation mode may alsobe attained by first having the pipes 3 and 9 blown through with thefluid in gaseous state.

[0028] As FIG. 3 shows, it is also possible to couple resevoir 7directly to the bottom end of the feedback duct 9. In this case,however, the reservoir is pressurized and must be capable ofwithstanding this. This may be solved as follows:

[0029] pressurized gas may be added by way of a cock 11. Said gas mustbe a gas different from butane, since butane condenses at a pressure inexcess of 2 bar, preferably a gas, such as nitrogen, which is incapableof forming an explosive mixture with the gas already present, which gasthen operates as a propellant. At the location of the gas/liquidtransition in the reservoir, there may also be placed a piston.Reservoir 7 now has the function of an overflow tank, such as with acentral-heating installation.

[0030] With larger differences in altitude than those which may bebridged by compressor 6, it is possible, as shown by FIG. 4, to fillfrom the air-relief cock 12. Now it is possible, in vessel 7 a, for thegaseous state and the liquid state of the butane to exist side by side.If the highest point is incapable of being attained, it is stillpossible, with butane, to attain 16 metres more of difference inaltitude than may basically be attained by the pump, namely, by placinga vacuum pump at the end of duct 3 near coupling piece 10.

[0031] In the feedback piece 10, there is space to let the cable 1through after it has passed the end of duct 3. After installation, theend of the cable is then well accessible for further processing. Fromthis situation, after uncoupling the feedback piece 10, the cable 1 iscapable of being still further installed by connecting a second inputdevice 4 to a next duct.

[0032] In the exemplary embodiment according to FIG. 5, cable 1 isconnected, by way of a coupling 14, to a towing wire 1 a. In thearrangement shown, at the output of the duct 3 there is provided for anoutput device 4 a having a pair of pressure rollers 5 a, 5 a′ and anexhaust opening 8 a for fluid. Essentially, the setup of device 4 a isthe same as that of device 4. To the input device 4, there is fed liquidcarbon dioxide, by way of a cock 16, from a cylinder 15. Since the gasin the cylinder is already pressurized, no compressor is required. Byheating the cylinder 15, the pressure therein is capable of beingmaintained. By opening the cock 16 a little, there is firsts admittedcarbon dioxide in gaseous form. By way of duct 3, this flows to theoutput device 4 a, where it may be collected in a cylinder 15 a,possibly by way of a compressor 6 a. Subsequently, using a cock 16 a inthe supply pipe to cylinder 15 a, the pressure at the output of duct 3is set at a value in excess of 5 bar Subsequently, cock 16 is openedwider, until the desired operational pressure at the input end isattained. Once the duct is filled with liquid, or possibly before that,it is permitted to start the introduction of cable 1, pushing it usingwheels 5, 5′ of the input device 4 and pulling the towing wire 1 a withthe wheels 5 a and 5 a, of the output device 4 a. The liquid carbondioxide runs into cylinder 15 a, while the pressure at the end of duct 3is maintained in excess of 5 bar using cock 16 a. In doing so, use maypossibly be made of a compressor 6 a. It is also permitted to coolcylinder 16 a.

[0033] The invention will be explained below by reference to fiveexamples. In the first three examples, butane is used as a fluid, whilein the fourth and fifth examples, the fluid is CO₂.

EXAMPLE 1

[0034] This example deals with the blowing of standard optical fibreinto empty “loose-duct” cables. A cable consists of a number of ducts“twisted” into a cable, each duct having an inner diameter of 1 mm andan outer diameter of 1.5 mm. The cables may be produced as normaloptical-fibre cables, omitting the optical fibre and any filler present.Various of said “standard” cables may be connected one to another in a(branched) network. The optical fibres may then be introduced withoutwelding. In the exemplary calculation, there is assumed a duct length of500 m and a pressure difference of 12 bar.

[0035] In such a ductlet, there is introduced an optical fibre having astandard coating. It has a weight of W=0.00072 N/m (see Appendix 2) anda density ρ_(fibre)=1.5 g/cm³. The effective weight W_(f) in liquidbutane therefore is 0.00043 N/m. fiche friction coefficient f betweenoptical fibre and ductlet is 0.2. The pressure with respect to theatmospheric pressure amounts to 12 bar.

[0036] From formulas (1), (2) and (3) of Appendix 1, there follows aflow rate v=0.32 m/s and a volume flow of φ_(v)=2.4×10⁻⁴ l/s (Note: Inthe calculation, it was assumed that the pressure at the output withrespect to the atmospheric pressure is 2 bar. This is necessary tomaintain the butane in the liquid state.). From formula (1) in Appendix1, it follows that the Reynolds number is 1000, and therefore laminar.For the entraining force, it follows from formula (5) of Appendix 1that: dF_(b1)/dx=2×10⁻⁴ N/m. This is amply greater than the frictioncoefficient fW_(f)=0.9×10⁻⁴ N/m. The maximum feasible installationlength is therefore over 1100 m, while, for comparison's sake, 420 m maybe attained by blowing in. The fibre will approximately flow as fast asthe butane. The installation of 500 m takes as little as half an hour.There are required approximately 0.4 litres of liquid for flowingthrough, plus the same amount again for filling the ductlet. This is a“worst-case” situation, however: for the major part, filling occursduring the installation; in addition, the initial flow rate and theentraining force will be greater since the ductlet has not yet beenfilled with liquid over its entire length.

[0037] In order to be capable of conducting the fibre, and particularlyits end, through the continuous curve made by an encabled (twisted)ductlet, the bending radius must be amply in excess of 20 cm; this iseasily achieved.

EXAMPLE 2

[0038] A fibre bundle having a diameter D_(c)=2.5 mm, comprising 6 glassfibres, is installed in a duct having an outer diameter of 8 mm and aninner diameter of 6 mm, and a length of 5 km. The weight W=0.03 N/m, thedensity ρ_(fibre)=0.63 g/cm³ (lighter than water), therefore theeffective weight W_(f) in butane is 0.0015 N/m. The friction coefficientf between fibre bundle and duct amounts to 0.25. The pressure differenceover the duct amounts to 10 bar.

[0039] Assuming a turbulent flow, there follows a flow rate v=0.3 m/sand a volume flow Φ_(v)=7×10⁻³ l/s (again see Appendix 1, formulas (1),(2) and (3), once again subtracting 2 bar). The Reynolds number is 5400;the flow is therefore really turbulent. For the entraining force therefollows, using formula (4) of Appendix 1: dF_(b1)/dx=1.9×10⁻³ N/m. Thisis significantly higher than the friction force fW_(f) of 0.4×10⁻³ N/m.The theoretically highest attainable installation length, therefore,even exceeds 20 km! The fibre bundle will approximately flow as fast asthe butane. The installation of the 5 km will take almost 5 hours. Thereare required approximately 140 litres of liquid for flowing through,plus the same quantity again for filling the duct. This relates to the“worst-case” situation.

EXAMPLE 3

[0040] This example concerns the installation of a standardoptical-fibre cable in a duct having an outer diameter of 32 mm and aninner diameter of 26 mm and having a length of 1200 m at a pressuredifference of 8 bar, the butane being returned to the input of the duct.

[0041] From actual practice, it is known that large quantities of waterare hard to remove from a duct having such a large diameter.Particularly with underwater passages and other situations where theduct lies deeper in the soil, water remains behind.

[0042] The optical-fibre cable has a weight W=1 N/m, a rigidity B=1 Nm²,a diameter D_(c)=10 mm and a density ρ_(cable)=1.3 g/cm³. For theeffective weight W_(f) in butane, there then applies W_(f)=0.54 N/m. Forthe friction coefficient f between optical-fibre cable and duct, thereapplies f=0.2.

[0043] Assuming that the flow is turbulent, there follow a flow ratev=1.9 m/s and a volume flow Φ_(v)=0.9 l/s (see Appendix 1, this timewithout 2 bar being subtracted from the pressure, since recycling isinvolved). The Reynolds number is 148200. the flow therefore is indeedturbulent. For the entraining force, there follows 0.14 N/m. This isgreater than the friction force fW_(f)=0.11 N/m, but the speed ofinstallation will be lower, approximately 1 m/s. The installation thentakes about 20 minutes and there is more than 1000 l of liquid butanerequired. Recycling is therefore desirable indeed. For comparison'ssake: upon blowing in using air, in the same situation a length of 700 mis feasible.

EXAMPLE 4

[0044] This example concerns the installation of a cable in a ducthaving an outer diameter of 8 or 10 mm and an inner diameter of 6 or 8mm, respectively. CO₂ is conducted into the duct, the pressure at thebeginning being 12 bar and, at the end of the duct, 5 bar (triplepoint).

[0045] The used cable has a weight W=0.22 N/m, a rigidity B=0.1 Nm², adiameter D_(c)=5 mm and a density ρ_(cable)1.14 g/cm³. The effectiveweight of the cable in carbon dioxide W_(f)=0.008 N/m. To the frictioncoefficient between cable and duct, there applies f=0.2. The pushingforce F_(push)=100 N.

[0046] For the calculations, there was assumed a duct section having init oscillations with an amplitude A=5 cm and a period P=6 m, after each200 m a 90° curve and a bending radius R_(b)=1 m. In the event ofcalculations using software based on the theory described in thisapplication, for the installation using air there follows aninstallation length of approximately 600 m for both ducts, whichsignifies that the entraining forces of the flowing air play but asubordinate rôle. For install with running carbon dioxide, however,there follows an installation length of 2 km and 4 km for the 8/6 mm andthe 10/8 nm duct, respectively. In this case, therefore, the entrainingforces of the flow do play a major rôle. Since the weight of the cableis well adjusted to the density of the liquid, there are almost noforces left to stop the cable. As a result, the small forces experiencedin curves by the cable as a result of then rigidity thereof play anunmistakable rôle as well. For a smaller bending radius of the curves,R_(b)=0.5 m, the installation length therefore is reduced to 800 m and1800 m for the 8/6 mm and the 10/8 mm duct, respectively. The effect ofthe cable rigidity in the curves may be diminished by additionallypulling the cable head. The installation length then is 1700 m and 3300m at a bending radius R_(b)=0.5 m, and 3400 m and 5100 m for a bendingradius R_(b)=1 m, both for the 8/6 mm and the 10/8 mm duct,respectively.

[0047] In the event of an 8/6 mm duct having a length of 2 km, the flowrate v≈0.4 m/s and the volume flow Φ_(v)≈0.011 l/s. The Reynolds numberis 13200, or amply turbulent. The installation of the cable takes alittle over 83 minutes and there is a little more than 9 l of liquidcarbon dioxide required.

EXAMPLE 5

[0048] In this example, use is made of a combination of pulling andpushing, as shown in FIG. 5. In this example all parameters, with theexception of the pressure at the input of the duct, are the same as inFIG. 4. In this example, the entraining forces of the liquid are notused at all. The liquid is there only for (partly) letting the cablefloat. A liquid, such as carbon dioxide, admittedly must be kept flowingin order to keep the temperature sufficiently low, but if the cable ispulled with a velocity in the order of the flow rate of the liquid orover, or even in a direction opposite to the flow direction of theliquid, there are no longer involved entraining forces exercised by theliquid on the cable. From calculations there follows, in this case, witha pushing and pulling force of 100 N, an installation length of 1250 mand 1050 m with curves having a bending radius R_(b) of 1 m and 0.5 m,respectively. Said result is substantially equal for the 8/6 mm and the10/8 mm duct.

[0049] Appendix 1: Flow Through Duct

[0050] For the calculations below, use was made of the formulas offeredin the book “Installation of optical cables in ducts”, by W. Griffioen,Plumettaz, Bex (CH) 1993.

[0051] The flow through a duct is characterized by the Reynolds numberRe: $\begin{matrix}{{Re} = \frac{\rho \quad {vD}_{h}}{\mu}} & (1)\end{matrix}$

[0052] where v is the average speed, ρ is the density (1.3 kg/m³ forair, 1000 kg/m³ for water and 600 kg/m³ for liquid butane) and μ is thedynamic viscosity (1.8×10⁻⁵ Pas for air, 110×10⁻⁵ Pas for water and20×10⁻⁵ Pas for liquid methane) of the flowing medium and D_(h) thehydraulic diameter. The latter is equal to the inner diameter D_(d) ofthe duct and, for duct filled with cable having a diameter D_(c), equalto D_(d)−D_(c). For a Reynolds number smaller than 2000, the flow islaminar, otherwise it is turbulent. There occurs hysteresis, however: ifthe turbulent state is achieved from the laminar state, the speed at thesame pressure over the duct will be reduced. The pressure will initiallyhave to be reduced a great deal further before a laminar flow is againobtained. In the event of a pressure gradient dp/dx over the duct, theaverage speed v follows from: $\begin{matrix}{\frac{p}{x} = {{- C_{d}}\rho \quad \frac{v^{2}}{2D_{h}}}} & (2)\end{matrix}$

[0053] The drag coefficient C_(d) follows from Re:$C_{d} = {{\frac{64}{Re}\quad {dus}\quad \frac{p}{x}} = {- \frac{32\mu \quad v}{D_{h}^{2}}}}$

[0054] for laminar flow and$C_{d} = {{\frac{0,31}{{Re}^{1/4}}\quad {dus}\quad \frac{p}{x}} = {- \frac{{0,155}\mu^{1/4}\rho^{3/4}v^{7/4}}{D_{h}^{5/4}}}}$

[0055] for turbulent flow.

[0056] The volume flow Φ_(v) to be calculated with

Φ_(ν) =νπD _(d) ²/4  (3)

[0057] for a duct without cable and Φ_(ν)=νπ(D_(d) ²−D_(c) ²)/4 for aduct filled with cable. The pressure gradient in the duct is linear forliquid flows and non-linear for (compressible) gas flows:$\frac{p}{x} = \frac{( {1 - {p_{a}^{2}/p_{i}^{2}}} )p_{i}}{2l\sqrt{1 - {( {1 - {p_{a}^{2}/p_{i}^{2}}} ){x/l}}}}$

[0058] for gas flow.

[0059] The pressure gradient in the duct results in a force F_(b1) onthe cable present therein, which may be broken down into two components,the hydrostatic F_(hs) and the hydrodynamic F_(hd). For turbulent flow,there follows:$\frac{F_{hs}}{x} = {{\frac{\pi}{4}D_{c}^{2}\frac{p}{x}\quad {en}\quad \frac{F_{hd}}{x}} = {\frac{\pi}{4}{D_{c}^{\quad}( {D_{d} - D_{c}} )}\frac{p}{x}}}$

[0060] and therefore in total: $\begin{matrix}{\frac{F_{bl}}{x} = {\frac{\pi}{4}D_{c}D_{d}\frac{p}{x}}} & (4)\end{matrix}$

[0061] As to the hydrodynamic component it was assumed, for turbulentflow, that the speed is constant over the entire duct cross section(except for the laminar boundary layer) and the forces are evenlydistributed over the surfaces of the duct and the cable. With laminarflow, such is not the case; here the speed is largest in the middle andis reduced towards the walls (of cable and duct). The liquid willtherefore exert less effect on the part of the cable near the duct wall.In a worst-case assumption, which is approximated for cables which aresmall as compared to the duct, only the projection of the cable on theduct wall is included as an effective surface of the cable. As a result,the entraining force is reduced by a factor π. Summarizing, for laminarflow there follows: $\begin{matrix}{\frac{F_{bl}}{x} = {{\frac{\pi}{4}\lbrack {D_{c}^{2} + {\frac{1}{\pi}{D_{c}( {D_{d} - D_{c}} )}}} \rbrack}\frac{p}{x}}} & (5)\end{matrix}$

[0062] Appendix 2: Standard Coated Optical Fibre

[0063] The glass in a glass fibre consists of quartz glass (density ρ of2.4 g/cm³ and Young's modulus E of 72 Gpa) having a diameter of 125 μm.Surrounding it is a first layer of (soft) coating of U.V. acrylate(density ρ of 1.3 g/cm³ and Young's modulus E of 0.005 Gpa) up to adiameter of 187.5 μm. Around this again there is a final outer layer of(hard) coating of U.V. acrylate (density ρ of 1.3 g/cm³ and Young'smodulus E of 0.5 Gpa) up to a diameter of 250 μm.

[0064] In total, therefore, the glass fibre has a density ρ of 1.5g/cm³, as was found from direct weight measurements as well. TABLE IDensity ρ_(liq), vapour pressure P_(sat), boiling point T_(b) andviscosity η at various pressures for various liquids. P_(sat) T_(b)/ηT_(b)/η T_(b)/η T_(b)/η ρ_(liq) at (1 bar) (5 bar) (10 bar) (15 bar)running (kg/ 20° C. (° C./x ¹⁰⁻ (° C./x ¹⁰⁻ (° C./x ¹⁰⁻ (° C./x ¹⁰⁻medium m³) (bar) ³Pas) ³Pas) ³Pas) ³Pas) water 1000 100/1 ethane  546¹40 −88.6 −53 −32 propane  501²  8 −42.1/0.19    1.4/0.12   26.9/0.09butane  579²  2  −0.5   50   80 carbon 1100³ −78⁴ −57⁵/0.25 −40/0.18−28/0.15 dioxide ammo-  910  9 −33    5   26 nia freon- −30 12

1. Method for installing cables in ducts using a fluid, characterized inthat a fluid is used which, at the operational pressure and operationaltemperature applied at the installation, is in a liquid state, andwhich, at the ambient pressure and ambient temperature prevailing at theinstallation location, is in gaseous state.
 2. Method according to claim1, characterized in that the fluid at the end located opposite the inputend of the duct is returned to the input end by way of a return pipe. 3.Method according to claim 2, characterized in that the fluid in thegaseous state thereof is returned by the return pipe.
 4. Methodaccording to claim 2, characterized in that the fluid is returned by thereturn pipe in the liquid state thereof.
 5. Method according to claim 1,characterized in that the fluid at the end located opposite the inputend of the duct is collected in a reservoir.
 6. Method according to atleast one of the claims 1 to 5 inclusive, characterized in that, priorto the installation of the cable, the fluid is introduced into the ductin the gaseous state.
 7. Method according to at least one of the claims1 to 6 inclusive, characterized in that the cable is installed using acombination of mechanical pushing forces and pulling forces.
 8. Methodaccording to at least one of the claims 1 to 7 inclusive, characterizedin that the fluid is chosen from the group of HFKs, CFCs, ammonia,propane, butane or a mixture thereof.
 9. Method according to at leastone of the claims 1 to 7 inclusive, characterized in that the fluid isCO₂.
 10. Device for carrying out the method according to any of theclaims 1 to 9 inclusive, provided with means to couple a fluid flow tothe input end of the duct in order to fill the duct with the fluid, andwith means to introduce the cable into the input end of the duct,characterized in that there are provided means to pressurize the fluidand/or to lower it in temperature in order to bring the fluid to theliquid state, which means comprise a stock vessel and/or a compressorand/or cooling means, which compressor and/or cooling means are coupledto the input end of the duct.
 11. Device according to claim 10,characterized in that there is provided for a return pipe connecting theend located opposite the input end of the duct to an input of thecompressor.
 12. Device according to claim 10 or 11, characterized inthat the stock vessel is coupled to the compressor.
 13. Device accordingto claim 11, characterized in that the stock vessel is coupled to thereturn pipe in the vicinity of the compressor, and that there isprovided for means to pressurize the liquid in the vessel.
 14. Deviceaccording to claim 11, characterized in that the stock vessel iscoupled, by way of an element capable of being closed off, to the returnpipe in the vicinity of the end located opposite the input end of theduct.